Since RHEL based distros are almost always behind the Debian/Ubuntu in terms of component versions, you will find that this doesn't work on RHEL or CentOS 6 variants as the current version of upstart (at time of writing) doesn't support setuid/setgid. However it can be made to work with upstart with the following mods (just put the userid you want it run as in there). I've also diverted the logging output to a file as per RH convention:
start on (local-filesystems and net-device-up IFACE!=lo)
stop on runlevel [!2345]
# setuid "nonrootuser"
# setgid "nonrootuser"
exec 1>>/var/log/syncthing.log 2>&1
su - $USERID -c '/usr/local/bin/syncthing'
Hope this helps someone.